Growth and Geodesics of Thompson's Group F

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Brigham Young University - Provo

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Schofield, Jennifer L.
Brigham Young University - Provo
Thompson's group F; growth function; reduced pairs of trees; pipe systems; Mathematics
thesis / dissertation description
In this paper our goal is to describe how to find the growth of Thompson's group F with generators a and b. Also, by studying elements through pipe systems, we describe how adding a third generator c affects geodesic length. We model the growth of Thompson's group F by producing a grammar for reduced pairs of trees based on Blake Fordham's tree structure. Then we change this grammar into a system of equations that describes the growth of Thompson's group F and simplify. To complete our second goal, we present and discuss a computer program that has led to some discoveries about how generators affect the pipe systems. We were able to find the growth function as a system of 11 equations for generators a and b.